When I create a mesh and try to select a previous mesh, it selects them both as if they were one object
If you add a mesh while in Edit Mode, the mesh will be part to the selected object. In an object you can have many different meshes, even if they don't share any vertices.

If you want them to be two different objects, exit Edit Mode add the new mesh while in Object Mode.

Anyway, you can select the added mesh and separate it (Press P).

For a detailed explanation on the difference on creating objects in edit mode and object mode read: 
Why can&#39;t objects in Edit Mode have their own name?